Probabilistic Properties of Stochastic Volatility Models

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A functional limit theorem for dependent sequences with infinite variance stable limits (2010, background): “Then (Xn)n satisfies the strong mixing condition with geometric rate (see Davis and Mikosch [15]).”
Measures of serial extremal dependence and their estimation (2013, background): “This fact was proved in Mikosch and Samorodnitsky [47] for the distribution of X .”
Stable limits for sums of dependent infinite variance random variables (2009, background): “A combination of the results in Davis and Mikosch (13) for ARCH(1) and in Mikosch and Stărică (43) for GARCH(1, 1) with Proposition 4.5 above yields the following.”
Extreme Value Theory for GARCH Processes (2009, background): “Davis and Mikosch [9], Section 4, one can also derive the relation”